This doesn't answer your question ... but perhaps what you're asking might be independent of "mental illness", in which case advice for you -- about "following the 8 fold path" -- might be the same for you as for everyone.
I'm not sure whether (or which) "mental illness" is an issue at the moment, given that you say it is well treated by medication -- from your writing here you seem to me lucid and obviously not very disabled.
If you were anxious about meditation, possibly like this would be relevant -- Three Tips on Mindfulness from a Buddhist Psychiatrist:
For those with anxiety especially, the idea of being alone with one’s thoughts can be overwhelming at first. Epstein does not recommend that one buckle down and push through such moments. Rather, he relates a story of discussing meditation induced anxiety with the Dalai Lama’s physician to find that Buddhism was quite familiar with the phenomenon. For those who find meditation to be suffused with dread,
“Tibetan doctors have such afflicted patients do simple tasks like sweeping the temple halls or chopping vegetables in the kitchen rather than prescribing more meditation. They know that they treatment for meditation-induced anxiety disorders is less meditation, not more.”
If the idea of meditating just seems like too much, bring the same focused attention to bear on doing your household activities, and in the process you will find your mind settling down to rest.
I'm not saying you are anxious, only that this seems to me an example of the sort of adaptable advice -- adjusting to your specific condition -- that you might benefit from if you were able to find an experienced teacher.
As for "practising incorrectly and reaching states (of mind) that are unhelpful", again I don't know what to say, not that I'm an expert.
This might be a good question (that I still wouldn't know how to answer) even as a stand-alone question i.e. if it were asked decoupled/independent from any question of prior/preconceived mental illness.
Correct me if I'm wrong but I suspect that Buddhism doesn't even start with meditation.
So far I know I think it's said to start with "virtue" (see e.g. here or here) -- including being mindful of "the precepts" as perhaps a minimum or a good beginning, and a certain but not excessive "generosity" (or dana) too -- being harmless, moderate, self-restrained.
And perhaps Right View is maybe supposed to be primary, and I think that that might start not with meditation but by learning dhamma -- reading suttas, hearing dhamma talks.
In earlier times that would necessarily have meant meeting with people (Kalyāṇa-mittatā).
Should I start for example with meditation on impermanence, on mindfulness, or by attempting to reduce my desire?
For me it was a question like, "Why would I be suffering after a friend's death?" -- that kind of touches on those themes, e.g. "impermanence" and "desire" -- and "attachment", which is adjacent to desire, and the sense of "self" which is said to be another cause of suffering.
I haven't read that's one of the classic forms of meditation, but it (death) is one of the classic forms of suffering and incentive for many people.
Off the top of my head some of the classic forms of meditation are:
- Learn to concentrate (on the focus of meditation)
- Learn peace or to relax (by letting go)
- Learn to observe (the senses are impermanent)
- Learn not to lust (by concentrating on disadvantages and by not dwelling on the sign of what's attractive)
- Learn to be kind and not angry or selfish (by rehearsing to view everyone as a friend)
- And many more -- Dzogchen, maybe "just sitting, and this rather remarkable practice (all from different schools)
This is sometimes summarised as there being two forms, i.e. Tranquillity and Insight, of which you eventually need both
I really couldn't tell you how you should start.
Maybe the question is more how you should stop -- Brahmana Sutta -- perhaps that's not the right question either.
This might help -- Four stages of enlightenment -- a partial summary of doctrine of one of the major schools (Theravada). I mention it because you were asking about "reaching states (of mind) that are unhelpful", this article might give a hint or road-map about what states of mind are considered relatively enlightened.
Even then I'm not sure, there's an aspect of this or risk that it might be a bit selfish or anti-social, solitary.
I think the unhelpful states of mind might be what are called Kleshas.